The Justices heard oral arguments in an affirmative-action case that explores whether the flagship state university's admissions practices aimed at creating campus diversity violate the rights of some white applicants.

Abigail Noel Fisher sued the school after her application was rejected in 2008 when she was a high school senior in Sugar Land, Texas.

Fisher claimed the individualized, discretionary admission policies violated her rights, and favored African-American and Hispanic applicants over whites and Asian-Americans.

Fisher just missed the opportunity of automatic admission to the main campus at Austin for in-state students finishing in the top 10% of their high school graduating class. So, she had to compete in a separate pool. It is that selection process that is before the court.

Photos:Photos: Supreme Court cases that changed America

Photos:Photos: Supreme Court cases that changed America

Supreme Court cases that changed America – Hollingsworth v. Perry (2013): The Supreme Court dismissed an appeal over California's Proposition 8 on jurisdictional grounds. The voter-approved ballot measure barring same-sex marriage was not defended by state officials, but rather a private party. This ruling cleared the way for same-sex marriage in California to resume, but left open-ended the legal language of 35 other states barring same-sex marriage. Take a look at other important cases decided by the high court.

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Photos:Photos: Supreme Court cases that changed America

Supreme Court cases that changed America – United States v. Windsor (2013): When her wife died in 2009, Edith Windsor, 84, was forced to pay hundreds of thousands of dollars in estate taxes because her marriage was not recognized by the federal government's Defense of Marriage Act of 1996. The Supreme Court struck down the part of the law which denied legally marriage same-sex couples the same federal benefits provided to heterosexual spouses.

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Supreme Court cases that changed America – National Federation of Independent Business v. Sebelius (2012): The Supreme Court upheld most of the Affordable Care Act, the Obama administration's health care reform law, on June 28, 2012. The decision determined how hundreds of millions of Americans will receive health care.

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Supreme Court cases that changed America – Citizens United v. Federal Election Commission (2010): Activists rally in February 2012 to urge the Supreme Court to overturn its decision that fundamentally changed campaign finance law by allowing corporations and unions to contribute unlimited funds to political action committees not affiliated with a candidate.

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Supreme Court cases that changed America – Texas v. Johnson (1989): The Supreme Court overturned the decision that convicted Gregory Lee Johnson of desecrating a venerated object after he set an American flag on fire during a protest. The court ruled that Johnson (at right with his lawyer, William Kunstler) was protected under the First Amendment right to freedom of speech.

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Supreme Court cases that changed America – United States v. Nixon (1974): When President Richard Nixon claimed executive privilege over taped conversations regarding the Watergate scandal, the Supreme Court ruled that he had to turn over the tapes and other documents. The ruling set a precedent limiting the power of the president of the United States.

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Supreme Court cases that changed America – Roe v. Wade (1973): Norma McCorvey, identified as "Jane Roe," sued Dallas County District Attorney Henry Wade over a law that made it a felony to have an abortion unless the life of the mother was in danger. The court agreed with Roe and overruled any laws that made abortion illegal in the first trimester. Here, McCorvey, left, stands with her attorney Gloria Allred in 1989.

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Supreme Court cases that changed America – Miranda v. Arizona (1966): Ernesto Miranda confessed to a crime without the police informing him of his right to an attorney or right against self-incrimination. His attorney argued in court that the confession should have been inadmissible, and in 1966, the Supreme Court agreed. The term "Miranda rights" has been used since.

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Supreme Court cases that changed America – Gideon v. Wainwright (1963): The Supreme Court overturned the burglary conviction of Clarence Earl Gideon after he wrote to the court from his prison cell, explaining he was denied the right to an attorney at his 1961 trial.

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Supreme Court cases that changed America – Mapp v. Ohio (1961): The Supreme Court overturned the conviction of Dollree Mapp because the evidence collected against her was obtained during an illegal search. The ruling re-evaluated the Fourth Amendment, which protects citizens against unreasonable searches and seizures.

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Supreme Court cases that changed America – Brown v. Board of Education (1954): Nathaniel Steward recites his lesson surrounded by white classmates at the Saint-Dominique School in Washington. In Brown v. Board of Education, the Supreme Court ruled that it was unconstitutional to separate students based on race.

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Supreme Court cases that changed America – Korematsu v. United States (1944): Fred Korematsu, a Japanese-American man, was arrested after authorities found out that he claimed to be a Mexican-American to avoid an internment camp during World War II. The court ruled that the rights of an individual were not as important as the need to protect the country during wartime. In 1998, President Bill Clinton awarded Korematsu the Presidential Medal of Freedom.

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Supreme Court cases that changed America – Plessy v. Ferguson (1896): Homer Plessy was arrested when he refused to leave a whites-only segregated train car, claiming he was 7/8 white and only 1/8 black. The Supreme Court ruled that "separate but equal" facilities for blacks were constitutional, which remained the rule until Brown v. Board of Education in 1954.

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Supreme Court cases that changed America – Dred Scott v. Sandford (1857): When Dred Scott asked a circuit court to reward him his freedom after moving to a free state, the Supreme Court ruled that Congress didn't have the right to prohibit slavery and, further, that those of African-American descent were not protected by the Constitution.

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Supreme Court cases that changed America – Gibbons v. Ogden (1824): This was the first case to establish Congress' power to regulate interstate commerce. The ruling signaled a shift in power from the states to the federal government. Aaron Ogden, seen here, was given exclusive permission from the state of New York to navigate the waters between New York and certain New Jersey ports. When Ogden brought a lawsuit against Thomas Gibbons for operating steamships in his waters, the Supreme Court sided with Gibbons.

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Supreme Court cases that changed America – McCulloch v. Maryland (1819): In response to the federal government's controversial decision to institute a national bank in the state, Maryland tried to tax the bank out of business. When a federal bank cashier, James W. McCulloch, refused to pay the taxes, the state of Maryland filed charges against him. In McCulloch v. Maryland, the Supreme Court ruled that chartering a bank was an implied power of the Constitution. The first national bank, pictured, was created by Congress in 1791 in Philadelphia.

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Supreme Court cases that changed America – Marbury v. Madison (1803): When Secretary of State James Madison, seen here, tried to stop Federal loyalists from being appointed to judicial positions, he was sued by William Marbury. Marbury was one of former President John Adams' appointees, and the court decided that although he had a right to the position, the court couldn't enforce his appointment. The case defined the boundaries of the executive and judicial branches of government.

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Photos:Today's Supreme Court

Photos:Today's Supreme Court

The justices of the U.S. Supreme Court sit for their official photograph on October 8, 2010, at the Supreme Court. Front row, from left: Clarence Thomas, Antonin Scalia, Chief Justice John G. Roberts, Anthony M. Kennedy and Ruth Bader Ginsburg. Back row, from left: Sonia Sotomayor, Stephen Breyer, Samuel Alito Jr. and Elena Kagan. Scalia was found dead on February 13 at a Texas ranch he was visiting.

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Antonin Scalia – Justice Antonin Scalia was appointed by President Ronald Reagan in 1986 to fill the seat vacated by Justice William Rehnquist when he was elevated to chief justice. A constitutional originalist -- and a colorful orator -- Scalia was a member of the court's conservative wing. At the time of his death, Scalia was the court's longest-serving justice.

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John G. Roberts – In 2005, Chief Justice John G. Roberts was nominated by President George W. Bush to succeed Justice Sandra Day O'Connor as an associate justice. After Chief Justice William Rehnquist died, however, Bush named Roberts to the chief justice post. The court has moved to the right during his tenure, although Roberts supplied the key vote to uphold President Barack Obama's Affordable Care Act.

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Anthony M. Kennedy – Justice Anthony M. Kennedy was appointed to the court by President Ronald Reagan in 1988. He is a conservative justice but has provided crucial swing votes in many cases and authored landmark opinions, most notably in Obergefell v. Hodges, which legalized same-sex marriage nationwide.

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Clarence Thomas – Justice Clarence Thomas is the second African-American to serve on the court, succeeding Justice Thurgood Marshall when he was appointed by President George H. W. Bush in 1991. He is a conservative, a strict constructionist who supports states' rights.

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Ruth Bader Ginsburg – Justice Ruth Bader Ginsburg is the second woman to serve on the Supreme Court. Appointed by President Bill Clinton in 1993, she is a strong voice in the court's liberal wing.

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Stephen G. Breyer – Justice Stephen G. Breyer was appointed to the court in 1994 by President Bill Clinton and is part of the court's liberal wing.

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Samuel A. Alito Jr. – Justice Samuel A. Alito Jr. was appointed by President George W. Bush in 2006 and is known as one of the most conservative justices to serve on the court in modern times.

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Sonia Sotomayor – Justice Sonia Sotomayor is the court's first Hispanic and third female justice. She was appointed by President Barack Obama in 2009 and is regarded as a resolutely liberal member of the court.

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Elena Kagan – Justice Elena Kagan is the fourth female justice and is counted among the court's liberal wing. She was appointed in 2010, at the age of 50, by President Barack Obama and is the court's youngest member.

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JUST WATCHED

Is affirmative action constitutional?

MUST WATCH

Is affirmative action constitutional?02:26

The Supreme Court was clearly divided along ideological lines about whether affirmative action essentially has run its social and legal course, and should no longer be used in the way schools like Texas and others have done.

"You're trying to gut it," Justice Sonia Sotomayor said to Fisher's lawyer about the current legal precedent set in 2003.

She suggested that a university deserves some flexibility to create the kind of diverse campus environment it wants.

But Chief Justice John Roberts repeatedly asked, "What is the 'critical mass' of African-Americans and Hispanics at the university that you are working toward?"

When the school's lawyer said there was no specific number, Roberts pressed, "So how are we supposed to tell whether this plan is narrowly tailored to that goal? What is the logical end point?"

Justice Anthony Kennedy may prove the deciding or "swing" vote and could strike a compromise position -- possibly toss out the specific plan in question, while generally preserving the future use of affirmative action in more limited circumstances.

The school, with a 52,000-student body, defends its "holistic" policy of considering race as one of many factors -- including test scores, community service, leadership and work experience.

The Obama administration backed the school.

"Everyone competes against everyone else. Race is not a mechanical automatic factor. It's an holistic individualized consideration," said U.S. Solicitor General Donald Verrilli.

African-Americans in Texas as a whole represent about 12% of the population, but comprise about 5% of students at the University of Texas.

Much of the discussion during arguments surrounded the definition of "critical mass" -- how a university can use metrics to determine when it has reached the right mix of minority students to achieve diversity.

Justice Stephen Breyer wondered why his colleagues were even debating the issue following 2003 high court ruling that found state universities could narrowly set up admissions policies to consider an applicant's race.

The relevant high court case from nine years ago dealt with the University of Michigan's admission programs. The issue was divisive, with Justice Sandra Day O'Connor the swing vote upholding the law school's admissions criteria.

O'Connor, who is no longer on the bench, predicted affirmative action would no longer be needed in 25 years, offering a gentle push to institutions to keep that timeline in mind. Nearly a decade later, however, the newly-configured court may be poised to issue a more dramatic statement on the use of race.

The Texas school modified its admission policy to include race as one factor shortly after the 2003.

The court's more conservative members seized the initiative during arguments.

Roberts questioned how schools were to measure classroom diversity among students who come from mixed race families.

Justice Samuel Alito suggested it was unfair to place Asian-Americans into one group, when they come from a wide range of cultures-- Filipinos, Chinese, and Afghans among them.

"I thought that the whole purpose of affirmative action was to help students who come from underprivileged backgrounds, but you make a very different argument that I don't think I've ever seen before," he told Gregory Garre, representing the school.

Garre said the school wants minorities from different backgrounds.

"We go out of our way to recruit minorities from disadvantaged backgrounds," he said.

Kennedy jumped in.

"So what you're saying is that what counts is race above all," he said. "You want underprivileged of a certain race and privileged of a certain race. So that's race."

Kennedy added later: "I thought that the whole point is that sometimes race has to be a tie-breaker and you are saying that it isn't. Well, then, we should just go away. Then we should just say you can't use race, don't worry about it."